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Parametrix Construction

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Lévy Matters VI

Part of the book series: Lecture Notes in Mathematics ((LEVY,volume 2187))

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Abstract

In this chapter we present an existence result for Feller processes with symbols of form

$$\displaystyle{ q(x,\xi ) =\psi _{\boldsymbol{\alpha }(x)}(\xi ) }$$

where (ψ α ) α ∈ I is a family of continuous negative definite functions and \(\boldsymbol{\alpha }: \mathbb{R}^{} \rightarrow I\) a Hölder continuous mapping. We derive heat kernel estimates for the transition density and its time derivative and prove the well-posedness of the associated martingale problem.

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Notes

  1. 1.

    See the remark preceding Theorem 1.38.

  2. 2.

    We use the following convention: For a Hölder continuous function f we denote by ϱ( f) the Hölder exponent of f.

  3. 3.

    In the sense of finite-dimensional distributions.

  4. 4.

    Or C3’.

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Authors and Affiliations

  1. Institut für Mathematische Stochastik, Technische Universität Dresden, Dresden, Germany

    Franziska Kühn

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  1. Franziska Kühn
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Kühn, F. (2017). Parametrix Construction. In: Lévy Matters VI. Lecture Notes in Mathematics(), vol 2187. Springer, Cham. https://doi.org/10.1007/978-3-319-60888-4_3

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